Rec door not opening...concerned about carbon Monoxide

[Big Dawg1]

I have a 1990 300ZX 2+2 that I bought new many many years ago. Although it is no longer my daily driver, I still enjoy the car. One issue that I'm concerned about is that the Rec door is stuck shut (recirculating inside cabin air only). I've confirmed this by looking behind the glove box to see the door is in the shut position.
To get at the servo motor would require removing part of the dash which I'm not interested in doing.
My question is...although the Rec door is closed on this 300ZX, is fresh air still being pumped into the cabin? I'm concerned that if no outside air is entering the cabin and I get an exhaust leak, that carbon monoxide could build up to dangerous levels when I have the windows closed...which is all the time.
Am I safe?